The dq-theta Flux Map Model of Synchronous Machines

This paper presents the dqθ flux and torque maps modelling approach for synchronous machines, where the dependency of flux linkage and torque respect to the rotor phase angle θ is recorded to account for the effects of space harmonics and torque ripple. Using a FEA or experimental flux map identification session over a grid of id,iq operating points, the new dqθ maps are obtained via dedicated manipulation of the test results. Instead of averaging the dq flux linkage and torque waveform respect to θ, the θ related information, which is flux linkage undulation and torque ripple, is retained. The fundamental - or θ averaged - dq flux maps can be thus considered a subset of the extended dqθ approach. Magneto-static FEA simulations are used in the paper for describing the storage and manipulation procedure. With the new maps, the torque and flux waveforms are retrieved by bi-linear interpolation of the respective maps at any id,iq condition, including non-identified operating points. Moreover, the torque and flux maps of the machine after skewing can be calculated off-line in seamless time by off-line interpolation of the dqθ maps, without additional FEA simulation and for any skewing angle and number of slices. As a further validation, the presented procedures will be included into an open-source design environment, available on the web.